Large-scale genomic and transcriptomic profiles of rice hybrids reveal a core mechanism underlying heterosis

Background Heterosis is widely used in agriculture. However, its molecular mechanisms are still unclear in plants. Here, we develop, sequence, and record the phenotypes of 418 hybrids from crosses between two testers and 265 rice varieties from a mini-core collection. Results Phenotypic analysis shows that heterosis is dependent on genetic backgrounds and environments. By genome-wide association study of 418 hybrids and their parents, we find that nonadditive QTLs are the main genetic contributors to heterosis. We show that nonadditive QTLs are more sensitive to the genetic background and environment than additive ones. Further simulations and experimental analysis support a novel mechanism, homo-insufficiency under insufficient background (HoIIB), underlying heterosis. We propose heterosis in most cases is not due to heterozygote advantage but homozygote disadvantage under the insufficient genetic background. Conclusion The HoIIB model elucidates that genetic background insufficiency is the intrinsic mechanism of background dependence, and also the core mechanism of nonadditive effects and heterosis. This model can explain most known hypotheses and phenomena about heterosis, and thus provides a novel theory for hybrid rice breeding in future. Supplementary Information The online version contains supplementary material available at 10.1186/s13059-022-02822-8.

Parameter n is known as Hill coefficient. It governs the steepness of the curve between two inflection points of the input function. Usually, it is moderately steep, with n = 1 -4. The larger is n, the more step-like being the input function. Particularly, When n =1, hill function is equal to Michaelis Menten equation. As many functions in biology, the Hill function approaches a limiting value at a high level of X, rather than increase indefinitely.
For a repressor, the Hill function is a decreasing S-shaped curve, whose shape depends on three similar parameters: Hill input function for repressor (3) The production of Y is balanced by two processes, degradation (destruction by specific proteins in the cell) and dilution (the reduction in concentration due to the increase of cell volume during growth). The degradation rate is α deg , and the dilution rate is α dil , giving a total degradation plus dilution rate (in units of 1/time) of The change in the concentration of Y due to the difference between its production and degradation plus dilution, as described by a dynamic equation: At stead state, Y reaches a constant concentration Y st , the steady-state concentration can be found by solving for dY/dt = 0. The steady-state concentration is: If reached its maximal level, we can also write as： This makes sense: The higher is the production rate β, the higher will reach the steadystate concentration Y st . The higher is the degradation/dilution rate α, the lower is Y st . Now let us consider one single locus with allele A and a, which are or code some kind of receptor and can be regulated by ligand X. The product of allele A is Y 1 at steady-state under concentration [X 11 *] of active X (X 11 *), and that of a is Y 2 under concentration [X 22 *]. The production function of two alleles is expressed respectively as: Where α 1 > 0 and α 2 > 0 are the relative degradation rate.
Then, the product of two alleles at steady-state is respectively:   Scenario 2: two alleles of one polymorphic site under two independent backgrounds, that is, two alleles of one polymorphic site of the receptor can be bound by two respective and independent ligands as the backgrounds of the receptor (Fig. 3b, Additional file 1: Figure S28-S29). The ligand background concentration in two homozygotes and heterozygote will be 2[X 11 *] and 2[X 22 *], but X 11 * can only be allocated to allele A and X 22 * to allele a. The product of AA, aa and Aa at steady state will be: aa: Scenario 3: two alleles of one polymorphic site with shared background, that is, two alleles of one polymorphic site of the receptor can be bound by the same ligand as the background of the receptor (Additional file 1: Figure S31). The ligand background concentration in two homozygotes and heterozygote will be 2[X 11 *] = 2[X 22 *] = 2[X*]. If the ligand background X* was equally allocated to each of the two alleles in heterozygote as the simulation previously reported [86,87], the product of AA, aa and Aa at steady state will be: As our simulation indicated, the locus will always appear to be additive under the situation of equal allocation (X* = (X 11 * + X 22 *)/2). We proposed an optimal strategy to maximize the output of the heterozygote. Let S 1 +S 2 = 2[X*], S 1 and S 2 represent the ligand concentration allocated to allele A and a in heterozygote, respectively, when the product of heterozygote Y 12 is maximized at the ligand concentration 2[X*] (Fig. 3c-d  Aa: x a m n n n n n n Secondly, we consider the three scenarios under the situation that the ligand works as a repressor. Regarding Scenario 1, null allele vs one functional allele of one polymorphic site under one ligand background (Additional file 1: Figure S27). The product of AA, aa and Aa at steady state for negative regulation will be: Regarding Scenario 2, two alleles of one polymorphic site under two independent backgrounds (Additional file 1: Figure S30). The product of AA, aa and Aa at steady state for negative regulation will be: Regarding Scenario 3, two alleles of one polymorphic site with shared background (Additional file 1: Figure S34-35). The product of AA, aa and Aa at steady state for negative regulation will be: Simulation2: the model reflecting the performance of homozygotes and heterozygote of one locus simulated according to trimer ABA assembly The balance between genes involved in a biological complex is one important hypothesis about heterosis. The typical example for gene balance was reported by Balazs and coleagues [43]. Their studies indicated that mutation of the subunit in a trimer ABA complex can result in imbalance and thus is harmful, which might impact gene imbalance on dominance. However, these studies did not consider the effects from the counterpart background. Thus, we simulated the effects of complex background on dominance of one single polymorphic locus that codes A or B.
In the system of trimer ABA complex, A and B are monomers, AB is the bridge dimer without active function, the trimer ABA is the functional entity. The reaction among monomers, dimer and trimer could be illustrated by the following chemical formula: For simplicity, we consider a pseudo equilibrium state, that is: A and B were input once in an enclosed environment and no degradation was considered; after a period of time, a chemical equilibrium state will be achieved. Set S A and S B as the initial input concentration of A and B, k AB as the association rate from left to right in formula (18) We define association coefficient by the ratio of association to dissociation for two steps as: For given S A , S B , K 1 and K 2 , we solve the equation by using the optimize function in R and get the concentration of A, B, AB and ABA at the equilibrium state, the solutions of parent and F 1 was follow the same equations described above (Additional file 1: Figure S51).
We simulated two scenarios as following: